Which of the following are not correct?

Options

A. The escape velocity for the Moon is `6 km s^(-1)`.
B. The escape velocity from the surface of Moon is `v`.
The orbital velocity for a satellite to orbit very close to the surface of Moon is `v//2`
C. When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases.
D. The orbital velocity of a satellite revolving in as circular path close to the planet is independent of the density of the planet

Explanation

To determine which statements about the escape velocity and gravitational characteristics of the moon are correct or not, we need to analyze each statement systematically.

### Step 1: Understand Escape Velocity
The escape velocity (v) from a celestial body is given by the formula:
\[ v = \sqrt{\frac{2GM}{R}} \]
where:
- \( G \) is the universal gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( M \) is the mass of the celestial body,
- \( R \) is the radius of the celestial body.

### Step 2: Known Values for the Moon
For the moon:
- Mass \( M \approx 7.35 \times 10^{22} \, \text{kg} \)
- Radius \( R \approx 1.74 \times 10^6 \, \text{m} \)

Using these values, we can calculate the escape velocity for the moon.

### Step 3: Calculate Escape Velocity
Using the formula:
\[ v = \sqrt{\frac{2GM}{R}} \]
Substituting the known values:
\[ v = \sqrt{\frac{2 \times (6.674 \times 10^{-11}) \times (7.35 \times 10^{22})}{1.74 \times 10^6}} \]

Calculating this gives:
\[ v \approx 2.4 \, \text{km/s} \]

### Step 4: Analyze Each Statement
1. **The escape velocity for the moon is 6 km per second.** - **Incorrect**
2. **The escape velocity for the moon is 9.8 m per second.** - **Incorrect**
3. **The gravity of the moon is 1/6.** - **Correct** (The gravity on the moon is approximately 1/6th that of Earth)
4. **The approximate value of 2.14 is 1.6 m per second.** - **Incorrect**
5. **The escape velocity for the moon is 11.2 km per second.** - **Incorrect**
6. **The escape velocity for the moon is 2.4 km per second.** - **Correct**

### Conclusion
The statements that are not correct are:
- The escape velocity for the moon is 6 km per second.
- The escape velocity for the moon is 9.8 m per second.
- The approximate value of 2.14 is 1.6 m per second.
- The escape velocity for the moon is 11.2 km per second.